460

PHOTOMETRY AND ILLUMINATION

extreme rays of the projected beam. This assumption, however, is generally no more than, a convenient approximation to the truth, for it cannot always be assumed that the light is emitted in all directions from a single point. Often the light emitted in two different directions may behave as if it emanated from points which are separated by a distance far from negligible in comparison with the distance at which measurements have to be made.

§ (114) MINIMUM DISTANCE FOB PHOTOMETRIC MEASUREMENTS.—It may be generally assumed that the inverse square law holds for distances greater than fifty to four hundred times the diameter of the optical aperture with beams of 20° to 2" total divergence. As a very approximate guide it may be assumed that the inner limit of distance at which the beam has attained its final distribution is given by Kdl0, where 0 is the total angle, measured in degrees, of the cone of light formed by the beam, d is the diameter of the aperture, and K is a constant lying between COO and 1000.

This rule leads to the result that for such apparatus as motor-car headlights, where the diameter of the mirror is of the order of 10 inches and the divergence may be as little aa 5°, photometric measurements should always be made at least 100 feet away from the headlight. On the other hand, for a lens such as that used in a ship's navigation light, where the divergence may be as much as 20° with a lens height of 7 inches, a distance of about 20 feet is sufficient. In both these cases the chief difficulty is that of obtaining sufficient light to enable measurements to be made at these comparatively great distances, and very often a compromise has to be effected by making measurements at two shorter distances, and obtaining an approximation to the desired result by an extrapolation.

§(115) " EFFECTIVE " CANDLE - POWEE.— The information usually desired is that given by a curve of distribution of illumination on a screen placed so as to be perpendicular to the axis of the beam at a convenient distance from the source. This distribution may often be conveniently found by actual measurement of brightness at different portions of a white screen placed in the path of the light, using a form of portable illumination photometer (see p. 441). It is often more convenient, however, to keep the photometric appai-atus fixed in position and to move the source either in altitude or azimuth. Measurements of illumination can then be made by means of a photometer head fixed in a given position, with a comparison Jamp movable along a bench directed away from the source. Alternatively, the test surface of a portable photometer (see p. 441) may be fixed in a convenient position, and measurements of illumination at

this position may then be made for any desired orientation of the projector. The results may be expressed either directly in terms of illumination, or, by calculation, in terms of the candle-power which would be required of a point source placed in the position of the projector in order that it might produce at the screen the illumination actually measured there. The latter figure is generally termed the " effective candle-power " of the source in the direction considered.

§ (116) DISTRIBUTION CURVE POR BEAMS.— Whichever method of expressing the results is employed, the distance from the source at which the measurements have been made should always be stated. The results may be exhibited graphically by means of a curve in which the abscissae represent either illumination at a given distance or effective candle-power, while the ordinates are the corresponding angles of deviation from the axis of the apparatus. Such a curve, for a motor headlight beam of small divergence, is shown in the upper diagram of Fig. 70. The lower

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FIG. 70.

diagram is a polar curve for the same beam, and illustrates strikingly the failure of a polar diagram to give an intelligible representation of light distribution from any form of projection apparatus.

For photometry of small projection apparatus, auch as motor headlights, ships' light lenses and hand signalling lamps, the distances required by the formula given above do not generally exceed 100 feet, and consequently measurements can be carried on in the laboratory, where all that is required in addition to ordinary photometric equipment is a tilting table for movement in altitude, and a horizontal turn-table for variation of angle of azimuth. If the beam is roughly symmetrical about its centre, sufficient information is generally given by a curve, such as that shown in Fig. 70, representing the mean of measurements made across the horizontal and vertical diameters of the beam. If the beam is not symmetrical in shape, similar curves are obtained along other specified, lines of